There's no reason why we couldn't ship it into the middle of a desert if for some reason it couldn't go back into the sea, it wouldn't go very far once it was dumped. Conveniently, the places that rely/will rely on desalination the most happen to be desert countries.
I'd imagine the problem is the concentration of salt where the dumping occurs. There would need to be a system in place to spread the salt out over a large geographical area at concentrations that is not harmful.
It's not a global problem but a local one. Locally increased salinity and temperature can be a problem. You can drop a whole bunch of hot brine in the middle of the ocean to little effect, but the same is not true of a mangrove swamp or a bay.
That's what's happening to the fresh water after it's used, it goes back to the ocean. It's a closed cycle.
The scale of human water consumption to the volume of the sea is miniscule.
Global fresh water consumption is a fraction of a percent of the volume of the ocean ( https://www.wolframalpha.com/input/?i=((total+water+consumpt... )
There's no reason why we couldn't ship it into the middle of a desert if for some reason it couldn't go back into the sea, it wouldn't go very far once it was dumped. Conveniently, the places that rely/will rely on desalination the most happen to be desert countries.